Backtrack-free and backtrack-bounded search
(1988)

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"... . A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying ..."

. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...

"... A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic ..."

A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.

"... We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be asso ..."

We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain, and the two semiring operations (1 and 3) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can be used also in newly defined schemes.

"... Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, fo ..."

Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The problem we consider here is the solution maintenance problem in such a dynamic CSP (DCSP). We propose a new class of constraint recording algorithms called Nogood Recording that may be used for solving both static and dynamic CSPs. It offers an interesting compromise, polynomially bounded in space, between an ATMS-like approach and the usual static constraint satisfaction algorithms. 1 Introduction The constraint satisfaction problem (CSP) model is widely used to represent and solve various AI related problems and provides fundamental tools in areas such as truth...

"... We introduce a general framework for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated to each tuple o ..."

We introduce a general framework for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated to each tuple of values of the variable domain, and the two semiring operations (+ and x) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that some conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving schemes, thus allowing one both to formally justify many informally taken choices in existing schemes, and to prove that the local consistency techniques can be used also in newly defined schemes. 1

"... . We introduce two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discu ..."

. We introduce two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discuss the relationship between them. 1 Introduction Classical constraint satisfaction problems (CSPs) [19, 17] are a very expressive and natural formalism to specify many kinds of real-life problems. In fact, problems ranging from map coloring, vision, robotics, job-shop scheduling, VLSI design, etc., can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [8, 9, 18, 16, 19]. However, they also have evident limitations, mainly due to the fact that they are not very flexible when trying to represent real-life scenarios where the knowledge is not completely available nor crisp. In fact, in such situations, the abilit...

"... . Constraint satisfaction problems (CSP's) involve finding values for variables subject to constraints on which combinations of values are permitted. Symmetrical values of a CSP variable are in a sense redundant. Their removal will simplify the problem space. In this paper we give the principle ..."

. Constraint satisfaction problems (CSP&apos;s) involve finding values for variables subject to constraints on which combinations of values are permitted. Symmetrical values of a CSP variable are in a sense redundant. Their removal will simplify the problem space. In this paper we give the principle of symmetry and show that the concept of interchangeability introduced by Freuder, is a particular case of symmetry. Some symmetries can be computed efficiently thanks to the structure of the problem (neighborhood interchangeability is a kind of these symmetries). Therefore we show how such symmetries can be used by existing constraint propagation algorithms and introduce a backtrack procedure exploiting symmetries. Both theoritical analysis and expiriments indicate that our proposed approach is an improvment of neighborhood interchangeability use, and has very good behavior for pigeon-hole problems. 1 Introduction The finite domain constraint satisfaction problem (CSP) 2 is well known in Art...

"... Introduction Constraint satisfaction problems (CSPs) involve finding values for problem vari- ables subject to restrictions on which combinations of values are allowed. Fig. 2.1a presents an example: color the graph shown such that no vertices joined by an edge have the same color. The small letter ..."

Introduction Constraint satisfaction problems (CSPs) involve finding values for problem vari- ables subject to restrictions on which combinations of values are allowed. Fig. 2.1a presents an example: color the graph shown such that no vertices joined by an edge have the same color. The small letters indicate the choice of colors available at each vertex (a stands for aquamarine if you like). Here the variables are the vertices, the values for each variable are the set of colors available at the vertex and the constraints all happen to be the same: &quot;not same color&quot;. This is a binary CSP because all constraints involve two variables. For simplicity, we will assume here that our problems are presented as binary CSPs. One solution would be a for W, b for X, c for Y and a for Z. Fig. 2.1b shows a backtrack search tree that finds that solution. We say that the variable X is constrained by the variable Y, but not by the variable Z. We say that a for X is consistent with b for Y, but inconsi

) Ugo Montanari and Francesca Rossi Universit`a di Pisa, Dipartimento di Informatica Corso Italia 40, 56125 Pisa, Italy E-mail: fugo,rossig@di.unipi.it Abstract. In this extended abstract we describe our approach to modelling the dynamics of distributed systems. For distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. We use graphs to represent states of such systems, and graph rewriting to represent their evolution. The kind of graph rewriting we use is based on simple context-free productions which are however combined by means of the synchronization mechanism. This allows for a good level of expressivity in the system without sacrifying full distribution. Moreover, to approach the problem of combining productions together, we suggest to exploit existing techniques for constraint solving. This is based on the observation that the combination pr...

"... . In this paper we describe an approach to model the dynamics of distributed systems. For distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. The basic idea is ..."

. In this paper we describe an approach to model the dynamics of distributed systems. For distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. The basic idea is to use graphs to represent states of such systems, and graph rewriting to represent their evolution. The kind of graph rewriting we use is based on simple context-free productions which are however combined by means of a synchronization mechanism. This allows for a good level of expressivity in the system without sacrifying full distribution. To formally model this kind of graph rewriting, however, we do not adopt the classical graph rewriting style but a more general framework, called the tile model, which allows for a clear separation between sequential rewriting and synchronization. Then, since the problem of satisfying the synchronization requirements may be a complex combinatorial pro...